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No_ 49SS ~October 17, 1%4 NATURE 225 GENERALIZATION OF EPIDEMIC THEORY AN APPLICATION TO THE TRANSMISSION OF IDEAS By DR. WILLIAM GOFFMAN Center of Documentation and Communication Research, School of library Science, Western Reserve University AND DR. VAUN A. NEWILL School of Medicine, Western Reserve NE of the most -fundamentsl problems in the field O of infoI'JIUl.tion retrieval is that of determining the circumstances under which it might be necessary to introduce an information retrieval system as an aid to a given population of scientists. It is proposed. that this problem be examined in terms of the tra.nsmission and development of ideas within a population. Specifically, the transmission of ideas within a population will be treated 88 if it were the tre.nsmission of an infectious disease, that is, in terms of an epidemic process. An attempt will be made to indicate the role of information retrieval in the development of such a process. The EpidemiC Model - Since the spread of disease in a population is to be our model for the transmisaion of ideas, it is appropriate to disoU88 the essential prinoiples pertinent to this issue. These prinoiples are a part of epidemiology. The necess~- elements involved-in the process of the spread of infectious dise..... are those of: (1) a .pecified population; (2) an exposure to infectious material. The meinbera of the population belong to 1 of 3 bllSic 01"""". at given instant in time: (a) infective8. those members who are host to the infectious material; (b) 8U8ceptible8. thoSe who can become infectives ·given conta.ct with in· "tOOtious material; (0) removalB. those who have been zreInoved for one of a variety of reasons suoh as death. ~unity, .hospitalization. etc. These latter members may have been either susoeptibles or infectives at the time Of their removal_ n.e entire process is time-dependent, that is, a sequence 'events ocours which describes the process. An in~ '" uaI is exposed to infectious material either by direct ilo.ntact with an infective or through some intermediary i8Bt or vector. The exposed. person may either be resistant to the incoming organism. in whioh case the organism is d~, or may be infected by it, in which case the inVading organism proceeds on a course of development. ·TJie time interval in whioh the development takes place ii ea.lled the 'latenoy period' (or incubation period), that , Ii; the interval of ,time. necessary for a susceptible 1p be ~transfonned into an infective. In other words, the latency Plriod is the time between the receipt of infectious material /'~. 8 rJUBCeptible and the time at which he is in position 16-tlansmit infectious material to another susceptible, thus '~ting the process. An epidemio ocours when the prooess of susceptibles being transformed to infectives crOsses a certain threshold_ (The American Public Health ~cia.tion (1960) defined an epidemic as "the occurrence . . in' 8 oommwlity ... of a group of illnesses of similar nature. olearly in excess of normal expectation.") The process already described here does not take into (lOQ()unt the almost endless number of complexities which aotusUy arise. - It is a model, that is, an idealization of the real situation in which the complex process is reduced <to ita essential properties. an a University~ Cleveland. Ohio Transmission of Ideas as an 'Epidemic' Process In general. the 'epidemic' process oan be characterized as one of transition from one state (susceptible) to another (infective) where the transition is caused by eA-posure to some phenomenon (infectious material). The process need not be restricted to infectious diBeaBe but is a more general abstract process that might be applied to many situations. All that is needed is the appropriate interpretation of the process elements, that is, susceptibles, infectiv6S, removals, infectious material, intermediary host. latency period, disease, etc. People are susceptible to certain ideas and resistant to others. Once an individual is infeoted with an idea he may in turn, after some period of time, tra.nBID.it it to others. Such a process can result in an intellectual 'epidemio' (Table 1). For example, consider the development of psychoanalysis in the early part of this century. Freud was no less host to the infootioUB material of the 'disease' of psychoanalysis than the person carrying the organism capa.ble of transmitting a cold, nor is his writing leas of a 'vector' carrying the 'infectious material' than the mos· quito as a carrier of malaria. ", Moreover. Abraham, Ferenozi, Jung and Jones were no less 'susceptibles' who were infected by the ideas of Freud and who. after a certain latency period, themselves became 'infectivea t than are those iadividua1s infected by the droplete expressed by a cold oarrier. J ung might represent an example of acquired resistance to the disease while the resistance of the medical community of Vienna could represent innate immunity. The development of the psychoanalytic movement in the early part of the twentieth century was in its way no less an 'epidemio' than WllS the outbreak of influenza in 1917 and 1918. One can argue similarly that Darwin and evolution, Cantor and set theory. Newton and mechanics. and so on. were examples of 'epidemics' in the world o~ scientifio thought which were instigated by the introduotion of a single infective into a population. 'I'h6 analogy is J?-ot restricted to science; for examples suoh as Christ, Buddha, Moses and Mohammed can be cited. in the Table 1. ANALOGY BETWE.EN INnCTlOUS DISUSE JJfD INTELLECTUJ.L El'mEliliCS Elements of the epidemic proc~al5 HOlt Agent Infective .. EJemenu Interpreted 1n tenna of Infectioull dlaeat.e epidemic Intellectual epidemic Infectious material Caae of disease Susceptible Person who will be Infected ginn ef[octh-o contact Removal Vector Agent Death or lmmunlty Idea Author of paper Rellder of paper who will be infecred given effective oontact Death or lou oflnterellt Infectious material (as for Idea (al for boat.) host) Infective Vector harbouring the agent Paper containing usefulldenl Susceptible VectOr not harbouring the All papefll cClntalnInG' poten· 8{l:ent tlAlIy naefuJ Ideas Remo\-o.l Death Deletion or JOY 226 NATURE October 17, 1964 YOL. 204 religious field and other examples can be given almost be 88 broad 88 medicine. but might be epidemiology, and endlessly. mathematical epidemiology might be the suhfield (D). Although biological and intellectual epidemics can be N must be specified because D might develop into an considered ns special cases of a general process. there are 'epidemio' in some popula.tion N 1 but not in some other important differences. Intellectual epidemics are often N.. For oxample, the 'disease' of mathema.tical epidemi. desirable while biological ones usually are not. This ology will probably follow different oourses in the fields of difference. however. does not pertain to the structure of epidemiology, where it might become an 'epidemio'. and in the proceasea hut only to external factors whioh might the field of mathematics, where it probably will never be introduced. In one oase, one usually wishes to enhance become an 'epidemio'. An additional example from the the process, while in tho other to eliminate it. field of medicine might be the present epidemio of cancer Another important differonoe relates to the infectious of the lung among smokers that is certainly different from material. In the biological case the infective individual the pattern of development of the disease among nonproduces infectious material that closely resembles that smokers. . which started the process; there baa been little mutation Let N I be the set of a.uthol"8 who have written papors or change. Such is not the case with the intellectual in F a.t time t l , whore t. represents the starting time of the epidemio, for here BOme mutation or ohange of the original proC688. Let I. be the set of a.uthors who have written idea (infectious material) is prerequisite to placing it in papers in D at time teo Then I D represents the infective print. • popnlation at the beginning of the proceaa. Ifit is assumed Ideas are transmitted by personal communication or that there are n() removals a.t time t l • then 8.=N.-I I by puhlication. An epidemio cannot develop within a repreoent.. the suaeeptible popnlation at time,.. (Romovgiven population unless there is effective contact betw.!*Ul ·ala oonstitute .those membere of N who for BOme reason the susoeptibles and infectious material. The purpose of or other are no longer produoing papers in F.). . 'an infonnation retrieval system is to provide such effective Let I'. be the Bet of artioles produced in D .hy the oontaot whore it does not already exist. If such is the 088e, members of I. at time 10 and 8'. be the set of artic1eo an information retrieval sy&.em might be introduced even produced by the mefnbers of S. at I .. Than N'.= S'. + I', though such aystema are limited to the traosmission of oonatituteo the vector popnlation at time ,.. . ideas contained in published mate1'ial. . In general as the proceaa developB we have N =8 +I +B '. The essential question is : when is it desirable to intro· and N' = S' + I' + J!'. where B and B' repreoent removals. duce a formal information retrieval system into the At time t l , RI=O and B'.=O. -: intellectual activity of a population of scientists' Here The proceaa might be described as followa : A member the epidemic model may be of value for it permits the • of 8 is infected hy a meniber of I'. After a certain rephrasing of the queetion in terms' of epidemiological length of time (latency period) • becomes. an infective problema Buch as: (I) the tranamiasion and spread of and giVOB birth to new infections in N' which in turn may the disease; (2) the prediction of the epidemio COUl'B& ; infect other members of 8 and BO forth. In other words (3) the diacovery ofthe threBhold densities ofthepopnlation 8 produces a paper in D in which he oites a paper in I'. that might be paaead before an epidemio can develop. (The member of I' might contain more than one idea. The answer to these epidemiological questions might help (more than one type of 'infectious material') with reapect . to decide when an information retrieval system should to D. This same member of I' may contain ideas tha~ oould also infect members of a Bub·field other than D. be introduced. Our only interest in the member of I' is as a carrier of the 'infectious material' of D.) By producing this pBper Mathematical Models he has introduced a new infective in N'. He may also There ha.a been extensive development of abstract have cited papers in 8' 88~well,·so that he has infected or mathematical models in the theory of epidemics which associated members of 8' with the 'disease' D. The can. be put to general use. There are two types of models, appearance of the pa.per written by 8 in D indicates that namely, deterministic and stochastio. The deterministic he has made the transition from the susceptible to the approach represents the process as a system of differential infective state. equations while the stochastic approach describes· the Let ~ be the rate at which the members ofB become process as a finite state Markov process of either a discrete members of I. HODC6. 13 is the rate of infection in the or continuous parameter (the discrete parameter is popnlation N. Let~' be the rate of infection in the applicable where the latency poriod is constant, in which population N'. Then~' represent.. the rate at which case the infectives occur in generations) depending on the papers in S' are being oited by membel"8 of N who are physical situ'!otion. The stochastic representation, though producing papers in D. generally moro realistic, is mathematically more sophisAs the process develops with time, a. certain number of ticated. An excellent detailed treatment of this subject 8usccptibles and infectives in the host and vector popu· as related to infectious disease can be found in Baileyl. lations a.ro removed. In the case of the host population this removal might be loss of interest, death, etc. In the case of tho vector population it might be lack of citation A Deterministic Model due to deletion, inaccessibility. etc. Let y (y') be the The most natural avenue for exploring the process of rate of removal of infectives I (I') and let 8 (8') he the the tro.nsm.i::.sion of idOO8 within a population would seem rate of removal of susceptibles 8 (8'). Another aspect of the process as it develops is that new 'to be by way of the literature produced by the members of that population. Although the published article is supplies of susceptiblcs and infectiv08 are introduced into not the only way in which ideas can be transmitted, it the populations Nand N'. Let I' (1'.) be the rate at which does play an important part. We are interested in studying new susC6ptibles are introduced and let u (u') be the rate this role, for it is only in this respect that an information a.t which new infectivee are introduced. That is. ~ retrieval system can be justified at present. In terms of represents the rate at which new a.uthol"8 a.re introduced the epidemic process we arc therefore concerned with the in F but not in D, while 11' is the rate a.t which new papers tra.nsference of infectious material, that is, ideas. between are introduood in F but not in D. u represente the human hosts by means of an intermediary host or vector, rate at which new authors are introduced in D and u' the rate at which new papers are introduced into D. namely, the written article. The mathematical model to be presented includes the We wish to study the spread of the 'disease' D within the papulation N of the discipline F. Consider a. certA.in following states of transition of the host and vector field. (F) such as medicine and a certain Bubfield (D of F) populations within a short time interval de: the sus·. llUCh as medical epidemiology. The field (F) need not ceptible can rema.in a susceptible or become an infective .~ NO.4905 Table t. NATURE October 17, 1%4 BurE8 01' Tuxamo!f OJ' mJl B09T .4.lm Vscrolt POPtrL.UIONS· 8t.a£e loO which an lndlTldnal bdoDgl At time, At time t+ At ll/SaICt!pUble SUlIOCptible.1nfec::tlve or removal (2 Infeet:lvtl (3) Removal Infective or removal or removal, the infective can remain an infective or become a removal, and tho romoval must remain a. removal (Table 2). (To keep the mathematical model simple in this presentation. we are not permitting immunes to lose their immunity and to return to the susceptible population.) The latency period is asswned to be zero 80 that infective& occur continuously with time. If we assume homogeneous mixing among the members of the populations. the total process can be detenninistically described by the follo,....ing systems of differential equations : dS dt = -IlSI'- BS+{L IlSI'-yI +u dS' <It = -WS'I-BS'+{L' dI' dt =f)'S'I-y']' +u' dR' dR dt =yI+BS d:l =y'1'+8'8' - A threshold density of susceptibles can be obtained if we 8BSUID.e initial conditions of a single infectivo introe,luced into the host (N,l and vector (N',l populations at time t., that is, No=(S., I, O) and N'.=(8'o. I, O}. For an epidemic to develop from time to, the change in the number of infeotives in both the host and vector populations must be positive. Hence, from the above differential equations, we obtain the threshold pp' as follows : IlSI', > yI - u .. ~'S'I' > y'I' - u' "or ~'8.s'o > rr-yu'-yu+uu' .' and_, S,8', > . y-u (y;,U») (y' WU'») where· - - = p; and . ~. -r = y' -u' = pp' p' ,!thf;The epidemic curve whioh traoee the development of ~~ epidemio in time is given by the differential equation Ti."- other of epidemiologists. The 'disease' could be statisticel epidemiology. Then one might study the development of the field in terms of the interacting host and vector populations rother t.han in terms of single populations. Removal • In ll'llDeral the bOllt and vector populatlonll need not follow the &arne tran.s!Uonal patterna III In thlB ease. .~ = 227 P(ll with peake at the points iIi time where :~ =O' 88.1 ~ to infinity. that is, the size of the inf~tive population !J; after a long period of time. This discU88ion indicates ~ ~ epidemic can only develop from time t. provided ~ the product of the hoat end vector susceptible popalation exceeds the threshold pp'_ When a potential epidemic condition is present, the quantity of soientiste ~ information is suffioiently large that given effective oonteot en epidemic can develop. It is at this time that au information retrieval system might be introduced. 'If the population is already in an epidemic state, an ~ lDtormation retrieval system can be introduced in order • inaintain or inorease the frequency of effective contacte 1ietween susceptiblee end infeotivee_ Hence, the points .. at whioh an information retrieval system might be usefully ..introduced into a population are either at the initial ....pgint or the peak of the epidemio process or at a time l'then intensification of the epidemio process is desired. Other models different from the one we have presented could be constrncted that would interpret the epidemic hi~a different manner. For example, a model can be elaborated by introducing two int.Precting populations with rates of migration from one population to the other. One population might consist of biostatistioians and the :lII!i; size of the epidemio is given by the limit of I The Stochastic Approach In a stochastic model of the process described above tho actual number of now infectives occurring in a sbort time· interval ,,""ould be replaced with the probability of a new case occurring in that interval. This type of mathematical treatment is partioularly applicable when dealing with small populations. An epidemio process within a large population can be characterized as a collection of epidemic processes within sub.populationB. For example, the outbreak of an infectious di.sease in a community might more specifically be studied in terms of the household populations rather than the community as a whole. ~imilarly the intelleotual epidemio process within the population of a ce~in discipline could be studied in terms of its sub-populatiOns, that is, the 'disease' D of field F might be studied in t;.erma of the sub-fields of F, indioating, from the point of view of information retrieval, where intellectual epidemics are developing in a given discipline. Thua. a stochastic treatment of the epidemic procoases would in general be more desirable because the size of the populations being studied hae-been reduced. Unfortunately a stochastic model of an epidemic proceea with a vector population does not exist as far as we lmow.. Such a model is in need of development and attention is being given to this problem by the authors. Deterministic models, however. can be very usoful, partioularly in dealing with largo popuJetions, end experiments have been designed for the purpose of testing the model presented above. Discussion The construotion of 0. matheIIl&tical model of a oomplex physical situation" involves a certain amount of simplification. This is because the purpose of·the mathematicel model is the description and prediotion 'of the essential patterne of the phyeicel prooese end not the 80hievement of its complete analysis. A total understanding of tile procees requiree studies complementary to tho mathematicel ones. In the C880 of the infectious diseaeee this means biologicel, eoologioaJ; and cliniceJ investigations of the process as wen as mathematical; in the transmiMion of ideas, psychological, sociological, and linguistic studies. MathematiCB oannot indicate why exposure to a certain: virus will lead to infection or why a certain article will infect the reader with an idea. These important qU08tions must be answered elsewhere. However, mathematics can makeimportantcontn'butionstoward an understanding of the epidemio prooess if one keeps its limitations in mind. Of COUl'88, the usefulness of a mathematical model depende on: (I) boing able to solve the model; (2) obtaining reliable me88Ul'ements in order to test it. These are by no means negligible problems. since even the most simple representations present difficulties in obtaining alg~braio solutions. This is particularly true of the stochastic 0888. Additional problems are encountered in relation to defining popuJetions end obtaining reliable estimates of the parameters of the proC668. Although implementation of the epidemio model presents certain difficulties, much useful information concerning the transmission of ideas within a population might be obtained from the mathematicel appro80b. It could help in answering several questions that are basio for the design and operation of information re· trieval systems. These questions include: (l) Where and when is aCtivity within a given discipline doveloping into 'epidemio' proportions I (2) What is the expected 228 NATURE duration of this 'epidemic' activity T (3) 'What is the intensity of the 'epidemio" (4) What are the clo.ssio papers of a certain discipline, that is, the initial infecti vea of lUl outbreak 1 . Infonnation retrieval systems must be dynamic and should reflect the interactions between the researcher and the literature. It seems that the 'epidemic' approach is a workable method for describing and predicting cert.ain fundamental aspects of this interaction. Since the process of t~tting ideaa, 88 in the case of an infectious disease, is not a Single process within a population but a collection of interacting processes ,vithin October 17, 1964 VOL 204 Bub.populations, it would seem that the notion of an all. encompassing information retrieval system spanning the totality of knowledge should be replaced by the notion of small dynamio interrelated. systems that appear when needed and disappear when not needed. 'Epidemio' theory could have a wide range of applio. stions other thnn to the transmission of ideas. for example: to the study of certain ohronic diseases, divorces. accidenta, etc.• but these will not be elaborated on in this report. This work was supported by AFOSR grant 403-64 and U.S. Public Healtb Service grlUlt AM 063911--03. . I BalIey, X. T. I., PM Malktm4tWll Tht.orv 01 Epitkmiu (Grt.mD, 1980). NEWS and VIEWS Director of the Rowett Research Institute, Aberdeen: Dr. D. P. Cuthbertson, C.B.E. DR'-D. P. CtrnmERTSON, who will be retiring from the directorship of the Rowett Research Institute, Bucksburn, Aberdeen, on September 30, 1965, obtained his medical 'qualification in Glasgow and was for nearly twenty years leoturer in pathological chemistry 6nd physiological chemistry in the Royal Infinnary, Glasgow, lUld in the University of Glasgow. ·.... He beeame an authority on the biochemical effects of injury. and particularly on the acute depletion of protein following injury. His work on the prevention, and treatment of these changes became of espeoial importance during the Seoond World War. Cuthbertson worked for two years on the headquarters staif of the Medical Research Council before he was appointed director of the Rowett Research Institute, Aberdeen. in 1945. Under his influence the Institute grew rapidly in size and importance. and it is remarkable how Cuthbertson was able to direct so much work and produce an interesting report each year, summarizing work that had been published in 100 papers or more. He managed. however. to keep his own laboratory going and to give a number of lectures, which were published. He is an accomplished artist in water coloU1"8 and a keen golfer, and will clearly be able to find something to do when he retires. Dr. K. L. Blaxter DR. K. L. BLAXTER, at present head of the Nutrition Department, Hannah Dairy Research Institute, has been appointed to succeed Dr. Cuthbertson 88 director of the Rowett Research Institute. Dr. Blaxter. who is fortyfive, is a graduate of the University of Reading. He has been with the Hannah Dairy Research Institute since 1948. Before that he was a research officer at the Veterinsry Laboratory of the Ministry of Agriculture, Weybridge. During 1946-4-7 he was a Commonwealth Fund Fellow at the University of Illinois, Division of Nutrition. under Prof. H. H. Mitchell. With the exception of B period of war service v.-ith the Royal Artillery. he was a research assistant at the National Institute for Research in Dairying from his first graduation until going to Weybridge. Dr. Blaxter was Clive Behrens Lecturer in the Faculty of Agriculture, University of Leeds, during 1958-61; 1960 Thomas Baxter Prizemsn lUld Gold Medallist (for research on the nutrition of dairy cattle); National Research Council of Canada visiting lecturer to the Universities of British Columbia, Manitoba, SaskatchewlUl and Alberta in 1964; 1964 Royal Agricultural Society Gold Medallist (for research on the nutrition of farm livestock). He also gave the Fernhurst Lecture to the Royal Society of Arts in 1962, lectures to the Pro· fessors Council of the University, Uppsala, and to the Berlin Acndemy of Sciences, D.D.R., in 1962, and the third Samuel Brody Memorial Lecturer in·the University of :Missouri in 1964. Dr. Blaxter's work has been concerned with the nutritive value of home.grown foods for dairy cattle, food intake lUld food utilization, protein requirements and protein metabolism of dairy cattle and calves, hyperthyroidism in the ruminlUlt lUld tho use of iodinated protein, hypomagnes::e.mic tetany. vitamin E metabolism and muscular dy~trophy, energy metabolism and the energy requirements of cattle. and their relation to the environment. In 1962 his monograph entitled Tho Energy Metabolism oj Ruminants was puhlished. Dr. BJ.a.xter is a member of numerous learned societies and is a member of the joint Agricultural Research CouncilMedical Research Council Development Commission sub. committee on the monitoring of radioactive fall-out and of tho Working Party on Ruminants of the Agricultural Research Council's Technical Committee on Nutrient Requirements of Farm Livestock. Ministry of Aviation: Director of Engine Research and Development (I): Mr. -Dennis H. Mallinson MR. D. H. MALLINSON has been appointed director of engine research and development (I), Ministry of Aviation, in succession to Dr. J. Remfry, who has retired from the Public Service. Born in 1921, Mr. Mallinson was educated at Prince Henry's Grammar School, Otley, before going to the University of Leeds in 1939. He graduated with honours in applied mathematics in 1942 and was posted. 88 a junior scientifio officer to the Engine Department of the Royal Aircraft Establishment. As a member of the small but growing turbine division under Hayne Constant and W. R. Hawthorne, he was employed on engine performance investigations and particularly on the analysis of results from the flight tests of the pioneer jet aircraft. Transferring with the Royal Aircraft Establishment's Turbine Division to Power Jets, Reeearch and Development, Ltd.• he remained on engine performance work and was in charge of the Performance Section when the National Gas Turbine Establishment came into being. In 1949, following a period of about a year in which he acted. as technical and administrative assistant to the deputy director (Mr. Peter Lloyd, the present directA:?r-general of engine research and development), Mr. Mallinson became a member of the National Gns Turbine Establishment's ramjet research team Wlder Mr. R. P. Probert, concentrating first on thermodynamics but later encompassing fuel control systems and combustion development and finally assuming responsibility for the full-scale ramjet test vehicle programme. This programme was successfully completed in 1957 lUld from then until ssrly 1963 he was superintendent of the Engine Research Division at the 'National Gas Turbine Establishment in charge of work on propelling nozzles, control systems and highspeed ramjets. He transferred to Ministry of Aviation Headquarters, London, in· February 1963 88 888ist&nt director responsible for engine project assessment and continued in this post until receiving his present appointment. Dennis Mallinson is 0. district commissioner of the